Things you have to see

If you don't want to explore the mandelbrot set on your own, but just sitting in front of your browser and gasp, then you have to see the zooms provided by teamfresh or the same on vimeo.com. Otherwise you should try it, also.

Another deep zoom on vimeo.com is provided by Chris Korda. It impressively illustrates the coloring problem of pseudo-randomly scattered colors near the edge of the mandelbrot set.

On YouTube you can find some other impressive zooms:

To get an overview of typical patterns in the mandelbrot set you can visit the site miqel.com. It provides a Visual Guide To Patterns In The Mandelbrot Set and sample images for the different patterns. Additionally you'll find many interesting links, I'll not repeat here....

Another overview describes The Mandelbrot and Julia sets Anatomy including interactive applets.